The family of accused murderer Oscar Pistorius has denied reports he is feeling suicidal after shooting dead his girlfriend Reeva Steenkamp.

Pistorius "is in deep mourning but despite the tragic circumstances he is certainly not suicidal," said a statement issued by his uncle, Arnold Pistorius. He said Pistorius has support from his family.

"From the moment we were first informed about the dreadful event of the early morning of 14 February 2013, we have worked hard to come to terms with the sad news of Reeva Steenkamp's death and Oscar's role in it," said the uncle. "Oscar, broken as he currently is, believes he has a purpose in life and is working towards that."

The denial comes after reports that Pistorius was distraught and contemplating taking his life. Reports also said that Pistorius is facing financial ruin over the forthcoming murder trial. "The family doesn't deny that Oscar's legal expenses are massive and that he has sold off some of his investments, including his racehorses," said the statement. "Oscar will evaluate the cost situation on a day-to-day basis and make decisions as required."

The family statement came as Pistorius' lawyers filed an appeal in a South African court against bail restrictions. "The conditions appealed against are unwarranted and not substantiated by the facts," said the appeal. State prosecutors said they would contest it.

The appeal reflected the robust defence strategy of lawyers for Pistorius, who has been staying at his uncle Arnold's home in a Pretoria suburb since he was released on bail on February 22. It is a delicate balance because the Pistorius family has also sought to keep a low profile, expressing sorrow for the death of Ms Steenkamp. Pistorius says he mistakenly shot her, thinking she was an intruder in his home. Prosecutors argue he killed her intentionally after an argument.

In the appeal lawyers argued against the requirement that Pistorius surrender all passports and travel documents, and refrain from applying for such documents pending the end of his case.

The lawyers said evidence presented at the amputee athlete's bail hearing showed he is not a flight risk and should have the option of travelling outside South Africa as long as he has official permission. The appeal also said there was "no basis in fact or in law" justifying terms under which Pistorius must be supervised by a probation officer and a correctional official.

Officials will visit Pistorius at his uncle's home at least four times a month, according to James Smalberger, chief deputy commissioner of the department of correctional services.

In addition, the runner should be allowed access to the property at Silverwoods Country Estate where he shot Ms Steenkamp, once the state completes its investigations there within a "reasonable time limit," according to Pistorius' legal camp.